The primary reason for a) adding back depreciation and then b) deducting CapX payments is the timing difference between a) and b). This is primarily due to accounting regulations.
I use "CapX payment" b/c CapX is frequently financed rather than paid all at once.
Also, recognize that Depreciation is a pre-tax amount, whereas CapX is an after-tax amount.

EBITDA is supposed to be a measure that shows how valuable a business is prior to any capital structure / investment decisions and allow you to compare various businesses in different industries. In theory most of the items below EBITDA can be changed by financial management rather than operational changes. For example you could change the debt structure to reduce interest expense or lease instead of buy to reduce the depreciation expense.